Recurrent equations for the ruin probability of an insurance company for some risk models

Abstract

The stochastic risk model with random independent risks and premiums is studied. The recurrent relations for a calculation of the ruin probability of an insurance company in moments of insurance amounts are delivered. It is supposed that the insurance premiums are independent and identical distributed, and the insurance amounts satisfy to the same properties. The numbers of claim amounts and premiums are the independent Poisson’s processes which are independent of the claim amounts and premiums volumes. The case when the random premiums and the insurance amounts have the exponential distribution. Also the Gamma-distributions with an integer parameters are studied. The obtained results allow us to calculate the ruin probabilities in the infinite and in the finite time intervals. In the studied examples for the Gamma-distributions the graphics of the ruin probabilities during three years are presented. Refs 6. Figs 2. Tables 1.

Keywords:

ruin probability, risk model, stochastic premium and claim amount